Question

Evaluate the square root of the polynomial using factorisation method: $\frac{x^2-16x+64}{(a+b{)}^{10}}$

• A. $\frac{x+8}{(a+b{)}^5}$
• B. $\left|\frac{x+8}{(a+b{)}^5}\right|$
• C. $\left|\frac{x+8}{(a+b{)}^2}\right|$
• D. $\left|\frac{x-8}{(a+b{)}^5}\right|$

Answer 1

The correct option is D $\left|\frac{x-8}{(a+b{)}^5}\right|$

$\sqrt{\frac{x^2-16x+64}{(a+b{)}^{10}}}$
Factor of $x^2-16x+64=(x+8)(x+8)$
$\sqrt{\frac{x^2-16x+64}{(a+b{)}^{10}}}=\sqrt{\frac{(x+8{)}^2}{(a+b{)}^{10}}}$
$=$ $\sqrt{{\left(\frac{x+8}{(a+b{)}^5}\right)}^2}$
$=$ $\left|\frac{x+8}{(a+b{)}^5}\right|$